The first quartile is the middle value between the smallest
number and the middle number of the dataset. The second is the middle number of
the whole dataset. And the third is the middle value between the middle number
and the highest number of the dataset.

So the first quartile is at the 25% of our population of
numbers, the second at 50% and the third at 75%.

Excel since its 2010 version implements two methods of
calculating quartiles. Let’s try to explain the difference between them.

In this example we have a group of 12 numbers in ascending
order. The inclusive function uses the (n-1) method to calculate the quartiles
position. N is the total numbers we have which is 12 in our example, so n-1
equals 11.

If we multiply eleven by 0,25 we get the position of the
first quartile which is in our case is 2,75. In position 2 we have the number 8
and in position 3 the number 12. Using simple mathematics, we can calculate the
number in position 2.75 as the number 11. Using the same technique, we can
calculate the second and third quartile as well. Excel saves us all this
trouble with the inclusive version of quartile.

The exclusive version uses the (n+1) method to calculate the
quartiles position. N is 12 so N+1 equals 13.

We multiply this number by 0.25 as before we get the position of the first quartile which in our case is 3.25. Notice that all numbers are shifted one place to the right. This places the first quartile between 8 and 12 again but at a different relative position between them. So the first quartile now is the number 9. The same applies to the rest of the quartiles. The exclusive version of quartile does the heavy lifting and calculates the quartiles using this method.

Let us try to use these function in the following example.

Suppose we want to calculate the third quartile for all the
grades, of all the lessons in the table.

We use the inclusive version. Then select the table, and finally number three, for the third quartile.

We repeat the same procedure using the exclusive version. We select the table, and then number 3.

We notice the difference of the results they produce is
small.

For compatibility reasons the older Quartile function is still supported at the 2016 version of Excel.

We mentioned before that the quartiles reside at the 25, 50
and 75 percent of our population of numbers. What if we want to know the point
of the 90% of our dataset?